Lebesgue constants for Hadamard matrices

There are many advantages in the use of Hadamard matrices in digital signal processing. However one possible disadvantage is the so-called overflow, as measured by the associated Lebesgue constants. We show that for certain classes of recursively generated Hadamard matrices, there are logarithmic upper bounds for these constants. On the other hand, for some Hadamard matrices the Lebesgue constants are of order rootm These results have natural analogues in classical Fourier analysis.